There's lots of advice on how to structure a book, but less on how to structure series.

Book-level tension and series-level tension

When I say 'tension', you could think of it as 'problem to be solved' or 'villain' or 'plot engine' or 'stakes'. They're interchangeable.

Each book needs its own tension and resolution. And then the series as a whole needs its tension, which should be bigger, looming over the individual tension of the books.

You need to think about two kinds of plots: small ones nested into the big one, and providing cause-and-effect build-up to the Big Climax.

Each book should have its own self-contained story. The series has a longer, bigger arc with bigger stakes. The series-level climax should feel bigger than any individual book-level climax – in consequence, scope, and emotional weight.

(In Harry Potter, from the fourth book onward the focus comes off the book-level stories, and the series-level arc takes over.)

When one book ends, it should not end cleanly. The resolution of one conflict should create fallout that seeds the next one, and makes the Big Tension worse. All the smaller climaxes should lead to the Big Climax of the whole series in a chain of causation.

• Keep individual book arcs satisfying.
• Let consequences carry forward.
• Change the type of conflict, not just its size.
• Build toward a true series-level climax.

Keep it all fresh

• Change the cast. Kill people. Introduce people.
• Change the cast's relationships: enemies become allies. Allies become enemies.
• Reveals deepen the mystery or reframe it
• Change aspects of the world

Three problems

• Villain-of-the-week syndrome is where tension stays level. Each book follows the same rhythm of threat, struggle, resolution, reset, feeling stagnant.
• Power-creep aka Dragonball Z syndrome. Every new threat is bigger than the last: they fight off an army of 10k invaders, then 20k, then 50k. A dark lord in Book One, then a darker lord. At first this feels exciting. Eventually it starts to feel hollow, because scale stops meaning anything.
• Jumping the shark is called after an episode of Happy Days where Fonzie jumped over a shark on his motorcycle. This was a problem because then everything else that happened in Happy Days was dull by comparison. It's when the series peaks too early. You defeat the world-ending villain in book three, then spend the next two books on smaller conflicts. The story ran out of fuel.

All three problems are not problems when used in moderation –

• Villain-of-the-week syndrome is nice for a format of pure self-contained stories. It depends on format. Like if your business model is publish a comic every week for loyal fans, and continue that for 20 years, then you probably should keep the threat-level the same. Readers enjoy the comfort of familiarity.
• Power creep is good in moderation. The protagonists should grow stronger across the series to finally face the ultimate threat. The final threat should feel more dangerous than the smaller earlier threats.
• Jumping the shark can be ok for resolving one kind of plot before the climactic point of the series. See below on qualitative differences.

Obviously you're aiming for something more like this –

Qualitatively different plots

Those three problems (villain-of-the-week, power-creep, and jumping the shark) are to do with the INTENSITY of the tension. I was advising you to control the intensity in a way that keeps the reader on their toes. But you can also keep them excited with different TYPES of tension. (Buffy did a good job of this over 144 episodes.)

Mix up different kinds of conflict –

• romantic
• political intrigue
• moral dilemma
• social tension
• combat
• mystery and mystification

This works because you keep changing the problem the characters are solving, avoiding both escalation and de-escalation.

Some books can be more focused on one of these kinds of conflict than others. And they can be mixed. (e.g. The first book is 70% romance, 15% politics and 15% combat. The next book is 50% combat, 10% moral dilemma, 20% romance and 20% social tension)

Coherent series are not long

You might think that some writers publish 20+ books in a series.... but I've done some research and actually I'm not sure that has ever happened.

• Discworld is a series of 41 books? No, it is 41 books in the same world, divided into several series (e.g. the Unseen University series), none of which is longer than eight books. (The series within Discworld are explained here. In fact the longest series is eight short books (Discworld books are generally 60-80k words).
• Mistborn is (will be) three trilogies set in the same world
• All of Middle-Earth is really just five major books, plus fragments, shorts, and things by Christopher Tolkein.

I contend that it's inherently hard to keep everything well-structured beyond a certain scale.

Really really long-running things that go for decades (e.g. Batman) don't fix that problem. Instead they opt to deliberately make a mess of it, contradict yourself, have plot-holes. People don't necessarily care. Fine if that's what you want to do.

Here are more data on the lengths of series than you could wish for.

7-8 books seems to empirically be the upper limit. Trilogies are probably culturally powerful because that's a sweet spot.